International Encyclopedia of Systems and Cybernetics

A. RAPOPORT observed: "… mathematical truth, being established only with reference to propositions assumed to be true, cannot be shown to be true in the sense of scientific truth, that is, observationally or experimentally verifiable truth. Bertrand RUSSELL was not joking when he said that in mathematics we never know what we are talking about nor whether what we are saying is true" (1967, p.15).

The same point was made by A. EINSTEIN when he wrote: "As far as the laws of mathematics refer to reality they are not certain, and as far as they are certain, they do not refer to reality".

All this anyhow, does not need to be taken too hard: We just should remember that models – of any kind – are merely reflexions in human brains of (and on) a reality about which we cannot ever dream to attain absolute truth.

R. VALLÉE makes the point as follows: "Mathematics applies to physics because the objects and their properties recognized by experimental science in the physical world are selected, through relations that can be reproduced, in order to imply a mathematical definition which is amenable to calculation. Physical laws are merely the synthesis of the reproductible relations used for the definition" (1983b, p.563).

In some sense, mathematics are thus like an inquiry about the ways we make models of reality. When we start to look at reality in a different way, as we do as systemists, we are in need of new mathematical models, which are indeed appearing apace since 1965, and offer new ways to study systems structures and complex dynamics. Some older models also acquire new meanings and uses as for example graphs, matrixes and binary algebra.